Resistance to motion

From the standpoint of collector design and performance, the most important size-related property of a dust particfe is its dynamic behavior. Particles larger than 100 [Lm are readily collectible by simple inertial or gravitational methods. For particles under 100 Im, the range of principal difficulty in dust collection, the resistance to motion in a gas is viscous (see Sec. 6, Thud and Particle Mechanics ), and for such particles, the most useful size specification is commonly the Stokes settling diameter, which is the diameter of the spherical particle of the same density that has the same terminal velocity in viscous flow as the particle in question. It is yet more convenient in many circumstances to use the aerodynamic diameter, which is the diameter of the particle of unit density (1 g/cm ) that has the same terminal settling velocity. Use of the aerodynamic diameter permits direct comparisons of the dynamic behavior of particles that are actually of different sizes, shapes, and densities [Raabe, J. Air Pollut. Control As.soc., 26, 856 (1976)]. 

Friction factor, dimensionless Flow rate of one phase, GPM Aqueous phase flow rate, GPM Cy clone friction loss, expressed as number of cy clone inlet velocity heads, based on Drag or resistance to motion of body in fluid, poundals... 

This type can be illustrated by reference to the conditions existing in a properly designed plain bearing. If the two bearing surfaces can be separated completely by a fluid film, frictional wear of the surface is virtually eliminated. Resistance to motion will be reduced to a level governed largely by the viscosity of the lubricating fluid. 

F,j = Drag or Resistance to Motion of Body in Fluid, Poundals... 

The mean velocity of migration Vj depends on the external driving force = ZjFE and on the resistance to motion set up by the medium s viscosity. This retarding force as a rule is proportional to the velocity. Under the influence of the external force, the velocity will increase until it attains the value Vj where the retarding force VjQ (9 is the drag coefficient) becomes equal to the external driving force. Hence,... 

Early in the history of crystal dislocations, the lack of resistance to motion in pure metal-like crystals was provided by the Bragg bubble model, although it was not taken seriously. By adjusting the size of the bubbles in a raft, it was found that the elastic behavior of the raft could be made comparable with that of a selected metal such as copper (Bragg and Lomer, 1949). In such a raft, it was further found that, as expected, the force needed to form a dislocation is large. However, the force needed to move a bubble is too small to measure. 

Diffusion in Biological Fluids. Recall from Section 4.3.3.1 that polymer molecnles in dilute solutions can be characterized by a friction coefficient, f, which describes the resistance to motion throngh the solvent, and that the diffnsivity of these molecnles can be related to the friction coefficient by... 

In the procedure (ASTM D-2639), the sample is air dried prior to preparation and the temperature should not exceed 15°C (59°F) above room temperature, and drying should not be continued to the extent that oxidation of the coal occurs and the plastic properties of the coal are not altered by oxidation. The apparatus is then immersed in the heating bath and a known torque applied to the stirrer. During the initial heating no movement of the stirrer occurs, but as the temperature is raised, the stirrer begins to rotate. With increasing temperature, the stirrer speed increases until at some point the coal resolidifies and the stirrer is halted (Figure 7.4). The plastic properties of the sample are then measured by the resistance to motion of the fluid mass in the plastometer. 

Viscosity is the most important single fluid characteristic governing the motion of petroleum and petroleum products and is actually a measure of the internal resistance to motion of a fluid by reason of the forces of cohesion between molecules or molecular groupings. 

The work done in moving a particle through a distance dx against a frictional resistance to motion /(dx/df) can be equated with the resulting change in chemical potential given by the expression... 

FIG. 6-57 Drag coefficients for spheres, disks, and cylinders A = area of particle projected on a plane normal to direction of motion C = overall drag coefficient, dimensionless Dp - diameter of particle Fd = drag or resistance to motion of body in fluid Re = Reynolds number, dimensionless u = relative velocity between particle and main body of fluid (I = fluid viscosity and p = fluid density. (From Lapple and Shepherd, Ind. Eng. Chem., 32, 60S [1940].)... 

Test which is used to determine the relative wear-ball preventing properties of lubricants under boundary test lubrication conditions. Two values are reported - load wear index and weld point from two procedures EP test ASTM D 2596 and wear test ASTM D2266. There are four steel /2-inch balls. Three of the balls are held together in a cup filled with lubricant while the fourth ball is rotated against them. Resistance to motion. 

For a constant polysaccharide mass, an extended (random) coil exposes more surface area than does a helix, and a single helix exposes more than a double helix. The energy content of a polymer molecule is a property of its surface area. Thus, one consequence of a coil-to-helix transition is a diminution of the macromolecular exposed surface area and energy in compliance with the law of entropy. An increase in viscosity coincides with an increase in surface, inasmuch as the resistance to motion covers a wider area. 

Resistance to Motion—It has been demonstrated experimentally that Eq (2-3) represents fairly accurately the general law of resistance of bodies to motion. Resistance in the case of streamline or turbulent mo-... 

No sharp boundary exists between streamline and turbulent flow. In fact there is a rather extensive region where resistance to motion is a function of both the density and viscosity of the medium. For this intermediate region Allen (1900) found the value of n in Eq (2-3) to be V2, giving... 

Now consider a particle having a diameter d and vibrating with an amplitude equal to that of the stationary wave let its motion be in accordance with Stokes law. The resistance to motion will then be... 

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